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Your data matches 284 different statistics following compositions of up to 3 maps.
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Matching statistic: St001615
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
([],1)
=> 0
([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 2
Description
The number of join prime elements of a lattice.
An element $x$ of a lattice $L$ is join-prime (or coprime) if $x \leq a \vee b$ implies $x \leq a$ or $x \leq b$ for every $a, b \in L$.
Matching statistic: St001617
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(load all 3 compositions to match this statistic)
Values
([],1)
=> 0
([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 2
Description
The dimension of the space of valuations of a lattice.
A valuation, or modular function, on a lattice $L$ is a function $v:L\mapsto\mathbb R$ satisfying
$$
v(a\vee b) + v(a\wedge b) = v(a) + v(b).
$$
It was shown by Birkhoff [1, thm. X.2], that a lattice with a positive valuation must be modular. This was sharpened by Fleischer and Traynor [2, thm. 1], which states that the modular functions on an arbitrary lattice are in bijection with the modular functions on its modular quotient [[Mp00196]].
Moreover, Birkhoff [1, thm. X.2] showed that the dimension of the space of modular functions equals the number of subsets of projective prime intervals.
Matching statistic: St001621
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
([],1)
=> 0
([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> 2
Description
The number of atoms of a lattice.
An element of a lattice is an '''atom''' if it covers the least element.
Matching statistic: St000069
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(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],0)
=> 0
([(0,1)],2)
=> ([],1)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],2)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(1,2)],3)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(1,2),(2,3)],4)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,3),(1,2)],4)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(1,4),(3,2),(4,3)],5)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,3),(1,4),(4,2)],5)
=> 2
Description
The number of maximal elements of a poset.
Matching statistic: St001613
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The binary logarithm of the size of the center of a lattice.
An element of a lattice is central if it is neutral and has a complement. The subposet induced by central elements is a Boolean lattice.
Matching statistic: St001622
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(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The number of join-irreducible elements of a lattice.
An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
Matching statistic: St000080
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(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The rank of the poset.
Matching statistic: St000171
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(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
Description
The degree of the graph.
This is the maximal vertex degree of a graph.
Matching statistic: St000272
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
Description
The treewidth of a graph.
A graph has treewidth zero if and only if it has no edges. A connected graph has treewidth at most one if and only if it is a tree. A connected graph has treewidth at most two if and only if it is a series-parallel graph.
Matching statistic: St000454
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(load all 3 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> 2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
=> ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> 2
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
The following 274 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000778The metric dimension of a graph. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St001270The bandwidth of a graph. St001271The competition number of a graph. St001277The degeneracy of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001644The dimension of a graph. St001792The arboricity of a graph. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000258The burning number of a graph. St000528The height of a poset. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St001116The game chromatic number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001580The acyclic chromatic number of a graph. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001883The mutual visibility number of a graph. St001782The order of rowmotion on the set of order ideals of a poset. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000274The number of perfect matchings of a graph. St000310The minimal degree of a vertex of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001176The size of a partition minus its first part. St001340The cardinality of a minimal non-edge isolating set of a graph. St001345The Hamming dimension of a graph. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001512The minimum rank of a graph. St001623The number of doubly irreducible elements of a lattice. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000010The length of the partition. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000273The domination number of a graph. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000345The number of refinements of a partition. St000381The largest part of an integer composition. St000383The last part of an integer composition. St000384The maximal part of the shifted composition of an integer partition. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000469The distinguishing number of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000553The number of blocks of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St000822The Hadwiger number of the graph. St000935The number of ordered refinements of an integer partition. St001093The detour number of a graph. St001286The annihilation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001322The size of a minimal independent dominating set in a graph. St001330The hat guessing number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001389The number of partitions of the same length below the given integer partition. St001463The number of distinct columns in the nullspace of a graph. St001616The number of neutral elements in a lattice. St001642The Prague dimension of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001746The coalition number of a graph. St001820The size of the image of the pop stack sorting operator. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001963The tree-depth of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St001619The number of non-isomorphic sublattices of a lattice. St001626The number of maximal proper sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000068The number of minimal elements in a poset. St000181The number of connected components of the Hasse diagram for the poset. St000298The order dimension or Dushnik-Miller dimension of a poset. St000527The width of the poset. St000908The length of the shortest maximal antichain in a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000632The jump number of the poset. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000100The number of linear extensions of a poset. St000172The Grundy number of a graph. St000189The number of elements in the poset. St000286The number of connected components of the complement of a graph. St000307The number of rowmotion orbits of a poset. St000346The number of coarsenings of a partition. St000456The monochromatic index of a connected graph. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000722The number of different neighbourhoods in a graph. St000909The number of maximal chains of maximal size in a poset. St000910The number of maximal chains of minimal length in a poset. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St001029The size of the core of a graph. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001109The number of proper colourings of a graph with as few colours as possible. St001261The Castelnuovo-Mumford regularity of a graph. St001268The size of the largest ordinal summand in the poset. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001399The distinguishing number of a poset. St001581The achromatic number of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001779The order of promotion on the set of linear extensions of a poset. St000180The number of chains of a poset. St000379The number of Hamiltonian cycles in a graph. St000481The number of upper covers of a partition in dominance order. St000535The rank-width of a graph. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St000906The length of the shortest maximal chain in a poset. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001333The cardinality of a minimal edge-isolating set of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001393The induced matching number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001397Number of pairs of incomparable elements in a finite poset. St001664The number of non-isomorphic subposets of a poset. St001812The biclique partition number of a graph. St001827The number of two-component spanning forests of a graph. St000643The size of the largest orbit of antichains under Panyushev complementation. St000509The diagonal index (content) of a partition. St000668The least common multiple of the parts of the partition. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001128The exponens consonantiae of a partition. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001281The normalized isoperimetric number of a graph. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000480The number of lower covers of a partition in dominance order. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000659The number of rises of length at least 2 of a Dyck path. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001092The number of distinct even parts of a partition. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001587Half of the largest even part of an integer partition. St001651The Frankl number of a lattice. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000455The second largest eigenvalue of a graph if it is integral. St000477The weight of a partition according to Alladi. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000914The sum of the values of the Möbius function of a poset. St000526The number of posets with combinatorially isomorphic order polytopes. St001875The number of simple modules with projective dimension at most 1. St001890The maximum magnitude of the Möbius function of a poset. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St001095The number of non-isomorphic posets with precisely one further covering relation. St001568The smallest positive integer that does not appear twice in the partition. St000327The number of cover relations in a poset. St000634The number of endomorphisms of a poset. St000635The number of strictly order preserving maps of a poset into itself. St000656The number of cuts of a poset. St000699The toughness times the least common multiple of 1,. St000929The constant term of the character polynomial of an integer partition. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001331The size of the minimal feedback vertex set. St001570The minimal number of edges to add to make a graph Hamiltonian. St001638The book thickness of a graph. St000264The girth of a graph, which is not a tree. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001060The distinguishing index of a graph. St001112The 3-weak dynamic number of a graph. St001118The acyclic chromatic index of a graph. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001716The 1-improper chromatic number of a graph. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts. St001881The number of factors of a lattice as a Cartesian product of lattices. St000741The Colin de Verdière graph invariant. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001391The disjunction number of a graph. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001488The number of corners of a skew partition. St001624The breadth of a lattice. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St000907The number of maximal antichains of minimal length in a poset. St001738The minimal order of a graph which is not an induced subgraph of the given graph.
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